Multiply the following complex numbers: $({2+3i}) \cdot ({-3+i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({2+3i}) \cdot ({-3+i}) = $ $ ({2} \cdot {-3}) + ({2} \cdot {1}i) + ({3}i \cdot {-3}) + ({3}i \cdot {1}i) $ Then simplify the terms: $ (-6) + (2i) + (-9i) + (3 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -6 + (2 - 9)i + 3i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -6 + (2 - 9)i - 3 $ The result is simplified: $ (-6 - 3) + (-7i) = -9-7i $